A p-adic analogue of a formula of Ramanujan

Dermot McCarthy; Robert Osburn

doi:10.1007/s00013-008-2828-0

A p-adic analogue of a formula of Ramanujan

Dermot McCarthy, Robert Osburn

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.

Original language	English
Pages (from-to)	492-504
Number of pages	13
Journal	Archiv der Mathematik
Volume	91
Issue number	6
DOIs	https://doi.org/10.1007/s00013-008-2828-0
State	Published - Dec 2008

Keywords

Gaussian hypergeometric series
Supercongruences

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10.1007/s00013-008-2828-0

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